Back
 IJCNS  Vol.3 No.3 , March 2010
A New Global Asymptotic Stability Result of Delayed Neural Networks via Nonsmooth Analysis
Yaning Gu, Deyou Liu, Wenjuan Wu, Jingwen Zhang
Abstract: In the paper, we obtain new sufficient conditions ensuring existence, uniqueness, and asymptotic stability of the equilibrium point for delayed neural network via nonsmooth analysis, which makes use of the Lipschitz property of the functions. Based on this tool of nonsmooth analysis, we first obtain a couple of general results concerning the existence and uniqueness of the equilibrium point. Then we drive some new sufficient conditions ensuring global asymptotic stability of the equilibrium point. Finally, there are the illustrative examples feasibility and effectiveness of our results. Throughout our paper, the activation function is a more general function which has a wide application.
Keywords: Delayed Neural Networks, Global Asymptotic Stability, Nonsmooth Analysis
Cite this paper: nullY. Gu, D. Liu, W. Wu and J. Zhang, "A New Global Asymptotic Stability Result of Delayed Neural Networks via Nonsmooth Analysis," International Journal of Communications, Network and System Sciences, Vol. 3 No. 3, 2010, pp. 294-302. doi: 10.4236/ijcns.2010.33038.
References

[1]   S. Arik, “An improved global stability result for delayed cellular neural networks,” IEEE Transactions on Circuits and Systems Part I, Vol. 49, pp. 1211–1214, 2002.

[2]   T. L. Liao and F. C. Wang, “Global stability for cellular neural networks with time delay,” IEEE Transactions on Neural Networks, Vol. 11, pp. 1481–1484, 2000.

[3]   Q. Zhang, X. Wei, and J. Xu, “Global asymptotic stability analysis of neural networks with time-varying delays,” Neural Processing Letters, Vol. 21, pp. 61–71, 2005.

[4]   Q. Zhang, X. Wei, and J. Xu, “Global asymptotic stability of cellular neural networks with infinite delay,” Neural Network World, Vol. 15, pp. 579–589, 2005.

[5]   Q. Zhang, X. Wei, and J. Xu, “Stability analysis for cellular neural networks with variable delays,” Chaos, Solitons Fractals, Vol. 28, pp. 331–336, 2006.

[6]   R. A. Horn and C. A. Johnson, “Matrix analysis,” U. K. Cambridge University Press, Cambridge, 1985.

[7]   R. T. Rockafellar and R. J. B. Wets, “Variational analysis,” Springer-Verlag, Berlin Heideberg, Germany, 1998.

[8]   F. H. Clarke, “Optimization and nonsmooth analysis,” Wiley, New York, 1983.

[9]   B. H. Pourciau, “Hadamard theorem for locally Lips- chitzian maps,” Journal of Mathematical Analysis and Applications, Vol. 85, pp. 279–285, 1982.

[10]   A. L. Dontchev, H.-D. Qi, and L. Qi, “Convergence of Newton’s method for convex best interpolation,” Nume- rical Mathematik, Vol. 87, pp. 435–456, 2001.

[11]   L. Qi and J. Sun, “A nonsmooth version of Newton’s method,” Mathematical Programming, Vol. 58, pp. 353– 367, 1993.

[12]   H. K. Khalil, “Nonlinear systems,” Macmillan, New York, 1988.

[13]   R. M. Lewis and B. O. Anderson, “Intensitivity of a class of nonlinear comparetmental systems to the introduction of arbitrary time delays,” IEEE Transactions on Circuits and Systems Part I, Vol. CAS-27, pp. 604–612, 1980.

 
 
Top